LMFDB - Embedded newform 405.3.s.a.118.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(37,405)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([28, 9]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("405.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$408$
Relative dimension:	$34$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			118.8
Character	$\chi$	$=$	405.118
Dual form			405.3.s.a.127.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.205868 + 2.35308i) q^{2} +(-1.55539 - 0.274257i) q^{4} +(-4.64198 + 1.85797i) q^{5} +(-2.93406 - 2.05445i) q^{7} +(-1.47984 + 5.52284i) q^{8} +(-3.41632 - 11.3055i) q^{10} +(-3.30286 - 1.20214i) q^{11} +(-1.27699 - 14.5961i) q^{13} +(5.43832 - 6.48114i) q^{14} +(-18.6276 - 6.77989i) q^{16} +(1.65433 + 6.17406i) q^{17} +(1.16951 - 0.675215i) q^{19} +(7.72965 - 1.61677i) q^{20} +(3.50870 - 7.52443i) q^{22} +(4.93199 - 3.45342i) q^{23} +(18.0959 - 17.2493i) q^{25} +34.6088 q^{26} +(4.00016 + 4.00016i) q^{28} +(-36.1603 - 43.0941i) q^{29} +(1.46325 - 8.29852i) q^{31} +(10.1229 - 21.7087i) q^{32} +(-14.8687 + 2.62174i) q^{34} +(17.4369 + 4.08532i) q^{35} +(-5.71940 - 21.3451i) q^{37} +(1.34807 + 2.89095i) q^{38} +(-3.39188 - 28.3864i) q^{40} +(-16.5803 - 13.9125i) q^{41} +(19.5707 + 41.9694i) q^{43} +(4.80755 + 2.77564i) q^{44} +(7.11084 + 12.3163i) q^{46} +(-37.1779 - 26.0322i) q^{47} +(-12.3711 - 33.9892i) q^{49} +(36.8637 + 46.1322i) q^{50} +(-2.01687 + 23.0529i) q^{52} +(51.1073 + 51.1073i) q^{53} +(17.5654 - 0.556295i) q^{55} +(15.6883 - 13.1641i) q^{56} +(108.848 - 76.2164i) q^{58} +(-28.7190 - 78.9047i) q^{59} +(16.5080 + 93.6215i) q^{61} +(19.2259 + 5.15156i) q^{62} +(-19.6708 - 11.3569i) q^{64} +(33.0469 + 65.3822i) q^{65} +(-72.9564 + 6.38285i) q^{67} +(-0.879855 - 10.0568i) q^{68} +(-13.2028 + 40.1895i) q^{70} +(27.8020 - 48.1545i) q^{71} +(-34.7929 + 129.849i) q^{73} +(51.4043 - 9.06396i) q^{74} +(-2.00422 + 0.729477i) q^{76} +(7.22105 + 10.3127i) q^{77} +(-24.0782 - 28.6953i) q^{79} +(99.0658 - 3.13742i) q^{80} +(36.1506 - 36.1506i) q^{82} +(-4.86489 - 0.425622i) q^{83} +(-19.1506 - 25.5861i) q^{85} +(-102.787 + 37.4112i) q^{86} +(11.5270 - 16.4622i) q^{88} +(-79.3775 + 45.8286i) q^{89} +(-26.2402 + 45.4494i) q^{91} +(-8.61830 + 4.01878i) q^{92} +(68.9097 - 82.1234i) q^{94} +(-4.17429 + 5.30724i) q^{95} +(48.9432 - 22.8226i) q^{97} +(82.5262 - 22.1128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) $ 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.205868	+	2.35308i	−0.102934	+	1.17654i	0.752486	+	0.658608i	$0.228854\pi$
$2$	−0.205868	+	2.35308i	−0.102934	+	1.17654i	−0.855420	+	0.517934i	$0.826701\pi$
$3$		0			0
$3$		0			0
$4$	−1.55539	−	0.274257i	−0.388848	−	0.0685644i
$5$	−4.64198	+	1.85797i	−0.928395	+	0.371594i
$5$	−4.64198	+	1.85797i	−0.928395	+	0.371594i
$6$		0			0
$7$	−2.93406	−	2.05445i	−0.419151	−	0.293493i	0.344911	−	0.938635i	$-0.387909\pi$
$7$	−2.93406	−	2.05445i	−0.419151	−	0.293493i	−0.764062	+	0.645143i	$0.776798\pi$
$8$	−1.47984	+	5.52284i	−0.184980	+	0.690355i
$9$		0			0
$10$	−3.41632	−	11.3055i	−0.341632	−	1.13055i
$11$	−3.30286	−	1.20214i	−0.300260	−	0.109286i	0.187497	−	0.982265i	$-0.439963\pi$
$11$	−3.30286	−	1.20214i	−0.300260	−	0.109286i	−0.487757	+	0.872979i	$0.662185\pi$
$12$		0			0
$13$	−1.27699	−	14.5961i	−0.0982304	−	1.12278i	−0.872065	−	0.489390i	$-0.837219\pi$
$13$	−1.27699	−	14.5961i	−0.0982304	−	1.12278i	0.773834	−	0.633388i	$-0.218336\pi$
$14$	5.43832	−	6.48114i	0.388452	−	0.462938i
$15$		0			0
$16$	−18.6276	−	6.77989i	−1.16423	−	0.423743i
$17$	1.65433	+	6.17406i	0.0973137	+	0.363180i	0.997360	−	0.0726143i	$-0.0231342\pi$
$17$	1.65433	+	6.17406i	0.0973137	+	0.363180i	−0.900046	+	0.435794i	$0.856468\pi$
$18$		0			0
$19$	1.16951	−	0.675215i	0.0615530	−	0.0355376i	−0.468908	−	0.883247i	$-0.655352\pi$
$19$	1.16951	−	0.675215i	0.0615530	−	0.0355376i	0.530461	+	0.847710i	$0.322019\pi$
$20$	7.72965	−	1.61677i	0.386483	−	0.0808387i
$21$		0			0
$22$	3.50870	−	7.52443i	0.159486	−	0.342020i
$23$	4.93199	−	3.45342i	0.214434	−	0.150149i	−0.461425	−	0.887179i	$-0.652662\pi$
$23$	4.93199	−	3.45342i	0.214434	−	0.150149i	0.675859	+	0.737031i	$0.263773\pi$
$24$		0			0
$25$	18.0959	−	17.2493i	0.723836	−	0.689972i
$26$	34.6088			1.33111
$27$		0			0
$28$	4.00016	+	4.00016i	0.142863	+	0.142863i
$29$	−36.1603	−	43.0941i	−1.24691	−	1.48600i	−0.809925	−	0.586534i	$-0.800492\pi$
$29$	−36.1603	−	43.0941i	−1.24691	−	1.48600i	−0.436981	−	0.899471i	$-0.643952\pi$
$30$		0			0
$31$	1.46325	−	8.29852i	0.0472017	−	0.267694i	−0.952069	−	0.305884i	$-0.901048\pi$
$31$	1.46325	−	8.29852i	0.0472017	−	0.267694i	0.999271	+	0.0381899i	$0.0121592\pi$
$32$	10.1229	−	21.7087i	0.316342	−	0.678397i
$33$		0			0
$34$	−14.8687	+	2.62174i	−0.437313	+	0.0771101i
$35$	17.4369	+	4.08532i	0.498198	+	0.116723i
$36$		0			0
$37$	−5.71940	−	21.3451i	−0.154578	−	0.576895i	−0.999141	−	0.0414379i	$-0.986806\pi$
$37$	−5.71940	−	21.3451i	−0.154578	−	0.576895i	0.844563	−	0.535457i	$-0.179861\pi$
$38$	1.34807	+	2.89095i	0.0354756	+	0.0760777i
$39$		0			0
$40$	−3.39188	−	28.3864i	−0.0847971	−	0.709660i
$41$	−16.5803	−	13.9125i	−0.404397	−	0.339329i	0.417793	−	0.908542i	$-0.362804\pi$
$41$	−16.5803	−	13.9125i	−0.404397	−	0.339329i	−0.822190	+	0.569213i	$0.807248\pi$
$42$		0			0
$43$	19.5707	+	41.9694i	0.455132	+	0.976033i	0.991263	+	0.131898i	$0.0421073\pi$
$43$	19.5707	+	41.9694i	0.455132	+	0.976033i	−0.536132	+	0.844134i	$0.680115\pi$
$44$	4.80755	+	2.77564i	0.109262	+	0.0630827i
$45$		0			0
$46$	7.11084	+	12.3163i	0.154584	+	0.267746i
$47$	−37.1779	−	26.0322i	−0.791018	−	0.553877i	0.106781	−	0.994283i	$-0.465946\pi$
$47$	−37.1779	−	26.0322i	−0.791018	−	0.553877i	−0.897799	+	0.440406i	$0.854835\pi$
$48$		0			0
$49$	−12.3711	−	33.9892i	−0.252470	−	0.693657i
$50$	36.8637	+	46.1322i	0.737274	+	0.922645i
$51$		0			0
$52$	−2.01687	+	23.0529i	−0.0387859	+	0.443325i
$53$	51.1073	+	51.1073i	0.964289	+	0.964289i	0.999384	−	0.0350953i	$-0.0111735\pi$
$53$	51.1073	+	51.1073i	0.964289	+	0.964289i	−0.0350953	+	0.999384i	$0.511173\pi$
$54$		0			0
$55$	17.5654	−	0.556295i	0.319370	−	0.0101145i
$56$	15.6883	−	13.1641i	0.280149	−	0.235073i
$57$		0			0
$58$	108.848	−	76.2164i	1.87670	−	1.31408i
$59$	−28.7190	−	78.9047i	−0.486762	−	1.33737i	−0.903596	−	0.428385i	$-0.859083\pi$
$59$	−28.7190	−	78.9047i	−0.486762	−	1.33737i	0.416834	−	0.908983i	$-0.363140\pi$
$60$		0			0
$61$	16.5080	+	93.6215i	0.270623	+	1.53478i	0.752531	+	0.658557i	$0.228833\pi$
$61$	16.5080	+	93.6215i	0.270623	+	1.53478i	−0.481908	+	0.876222i	$0.660056\pi$
$62$	19.2259	+	5.15156i	0.310095	+	0.0830896i
$63$		0			0
$64$	−19.6708	−	11.3569i	−0.307356	−	0.177452i
$65$	33.0469	+	65.3822i	0.508414	+	1.00588i
$66$		0			0
$67$	−72.9564	+	6.38285i	−1.08890	+	0.0952665i	−0.617438	−	0.786619i	$-0.711829\pi$
$67$	−72.9564	+	6.38285i	−1.08890	+	0.0952665i	−0.471463	+	0.881886i	$0.656274\pi$
$68$	−0.879855	−	10.0568i	−0.0129390	−	0.147894i
$69$		0			0
$70$	−13.2028	+	40.1895i	−0.188611	+	0.574136i
$71$	27.8020	−	48.1545i	0.391578	−	0.678232i	−0.601080	−	0.799189i	$-0.705263\pi$
$71$	27.8020	−	48.1545i	0.391578	−	0.678232i	0.992658	+	0.120956i	$0.0385961\pi$
$72$		0			0
$73$	−34.7929	+	129.849i	−0.476616	+	1.77875i	0.138550	+	0.990355i	$0.455756\pi$
$73$	−34.7929	+	129.849i	−0.476616	+	1.77875i	−0.615165	+	0.788398i	$0.710911\pi$
$74$	51.4043	−	9.06396i	0.694652	−	0.122486i
$75$		0			0
$76$	−2.00422	+	0.729477i	−0.0263714	+	0.00959839i
$77$	7.22105	+	10.3127i	0.0937798	+	0.133931i
$78$		0			0
$79$	−24.0782	−	28.6953i	−0.304788	−	0.363232i	0.591810	−	0.806077i	$-0.298414\pi$
$79$	−24.0782	−	28.6953i	−0.304788	−	0.363232i	−0.896598	+	0.442845i	$0.853969\pi$
$80$	99.0658	−	3.13742i	1.23832	−	0.0392177i
$81$		0			0
$82$	36.1506	−	36.1506i	0.440861	−	0.440861i
$83$	−4.86489	−	0.425622i	−0.0586131	−	0.00512798i	0.0578115	−	0.998328i	$-0.481588\pi$
$83$	−4.86489	−	0.425622i	−0.0586131	−	0.00512798i	−0.116425	+	0.993200i	$0.537143\pi$
$84$		0			0
$85$	−19.1506	−	25.5861i	−0.225301	−	0.301013i
$86$	−102.787	+	37.4112i	−1.19519	+	0.435014i
$87$		0			0
$88$	11.5270	−	16.4622i	0.130988	−	0.187070i
$89$	−79.3775	+	45.8286i	−0.891882	+	0.514928i	−0.874557	−	0.484922i	$-0.838848\pi$
$89$	−79.3775	+	45.8286i	−0.891882	+	0.514928i	−0.0173241	+	0.999850i	$0.505515\pi$
$90$		0			0
$91$	−26.2402	+	45.4494i	−0.288354	+	0.499444i
$92$	−8.61830	+	4.01878i	−0.0936772	+	0.0436824i
$93$		0			0
$94$	68.9097	−	82.1234i	0.733082	−	0.873654i
$95$	−4.17429	+	5.30724i	−0.0439399	+	0.0558657i
$96$		0			0
$97$	48.9432	−	22.8226i	0.504569	−	0.235284i	−0.153630	−	0.988128i	$-0.549096\pi$
$97$	48.9432	−	22.8226i	0.504569	−	0.235284i	0.658199	+	0.752844i	$0.271319\pi$
$98$	82.5262	−	22.1128i	0.842104	−	0.225641i
$99$		0			0
$100$	−32.8770	+	21.8665i	−0.328770	+	0.218665i
$101$	−15.1212	−	85.7564i	−0.149714	−	0.849073i	−0.963460	−	0.267852i	$-0.913686\pi$
$101$	−15.1212	−	85.7564i	−0.149714	−	0.849073i	0.813746	−	0.581221i	$-0.197425\pi$
$102$		0			0
$103$	61.4201	+	28.6406i	0.596311	+	0.278064i	0.697250	−	0.716828i	$-0.254407\pi$
$103$	61.4201	+	28.6406i	0.596311	+	0.278064i	−0.100939	+	0.994893i	$0.532185\pi$
$104$	82.5018	+	14.5473i	0.793286	+	0.139878i
$105$		0			0
$106$	−130.781	+	109.738i	−1.23378	+	1.03527i
$107$	−129.856	+	129.856i	−1.21361	+	1.21361i	−0.243779	+	0.969831i	$0.578387\pi$
$107$	−129.856	+	129.856i	−1.21361	+	1.21361i	−0.969831	+	0.243779i	$0.921613\pi$
$108$		0			0
$109$		−	143.122i		−	1.31304i	−0.754308	−	0.656521i	$-0.772027\pi$
$109$		−	143.122i		−	1.31304i	0.754308	−	0.656521i	$-0.227973\pi$
$110$	−2.30714	+	41.4473i	−0.0209740	+	0.376793i
$111$		0			0
$112$	40.7255	+	58.1621i	0.363621	+	0.519304i
$113$	−141.780	−	66.1129i	−1.25469	−	0.585070i	−0.322337	−	0.946625i	$-0.604468\pi$
$113$	−141.780	−	66.1129i	−1.25469	−	0.585070i	−0.932351	+	0.361555i	$0.882246\pi$
$114$		0			0
$115$	−16.4778	+	25.1942i	−0.143286	+	0.219080i
$116$	44.4245	+	76.9455i	0.382970	+	0.663323i
$117$		0			0
$118$	191.582	−	51.3342i	1.62357	−	0.435035i
$119$	7.83038	−	21.5138i	0.0658015	−	0.180788i
$120$		0			0
$121$	−83.2276	−	69.8363i	−0.687832	−	0.577159i
$122$	−223.698	+	19.5710i	−1.83359	+	0.160418i
$123$		0			0
$124$	−4.55186	+	12.5061i	−0.0367085	+	0.100856i
$125$	−51.9521	+	113.692i	−0.415616	+	0.909540i
$126$		0			0
$127$	−21.4186	−	5.73910i	−0.168651	−	0.0451898i	0.173506	−	0.984833i	$-0.444491\pi$
$127$	−21.4186	−	5.73910i	−0.168651	−	0.0451898i	−0.342156	+	0.939643i	$0.611157\pi$
$128$	85.7287	−	122.433i	0.669755	−	0.956510i
$129$		0			0
$130$	−160.653	+	64.3021i	−1.23579	+	0.494631i
$131$	−40.7506	+	231.108i	−0.311073	+	1.76418i	0.282368	+	0.959306i	$0.408880\pi$
$131$	−40.7506	+	231.108i	−0.311073	+	1.76418i	−0.593441	+	0.804877i	$0.702231\pi$
$132$		0			0
$133$	−4.81859	−	0.421572i	−0.0362300	−	0.00316972i
$134$		−	172.986i		−	1.29094i
$135$		0			0
$136$	−36.5465			−0.268724
$137$	−2.01043	+	22.9793i	−0.0146746	+	0.167732i	−0.999996	−	0.00298038i	$-0.999051\pi$
$137$	−2.01043	+	22.9793i	−0.0146746	+	0.167732i	0.985321	+	0.170712i	$0.0546069\pi$
$138$		0			0
$139$	−139.754	−	24.6424i	−1.00543	−	0.177284i	−0.353394	−	0.935475i	$-0.614972\pi$
$139$	−139.754	−	24.6424i	−1.00543	−	0.177284i	−0.652033	+	0.758191i	$0.726083\pi$
$140$	−26.0008	−	11.1365i	−0.185720	−	0.0795463i
$141$		0			0
$142$	107.588	+	75.3339i	0.757662	+	0.530521i
$143$	−13.3289	+	49.7441i	−0.0932090	+	0.347861i
$144$		0			0
$145$	247.923	+	132.857i	1.70981	+	0.916257i
$146$	−298.383	−	108.602i	−2.04372	−	0.743853i
$147$		0			0
$148$	3.04186	+	34.7686i	0.0205531	+	0.234923i
$149$	−135.284	+	161.225i	−0.907946	+	1.08205i	0.0883531	+	0.996089i	$0.471840\pi$
$149$	−135.284	+	161.225i	−0.907946	+	1.08205i	−0.996299	+	0.0859583i	$0.972605\pi$
$150$		0			0
$151$	−238.024	−	86.6336i	−1.57632	−	0.573732i	−0.601917	−	0.798558i	$-0.705596\pi$
$151$	−238.024	−	86.6336i	−1.57632	−	0.573732i	−0.974399	+	0.224826i	$0.927819\pi$
$152$	1.99842	+	7.45821i	0.0131475	+	0.0490672i
$153$		0			0
$154$	−25.7533	+	14.8687i	−0.167229	+	0.0965498i
$155$	8.62601	+	41.2402i	0.0556517	+	0.266066i
$156$		0			0
$157$	−37.1814	+	79.7357i	−0.236824	+	0.507871i	−0.988418	−	0.151755i	$-0.951508\pi$
$157$	−37.1814	+	79.7357i	−0.236824	+	0.507871i	0.751594	+	0.659626i	$0.229285\pi$
$158$	72.4795	−	50.7507i	0.458731	−	0.321207i
$159$		0			0
$160$	−6.65631	+	119.579i	−0.0416020	+	0.747371i
$161$	−21.5656			−0.133948
$162$		0			0
$163$	88.1454	+	88.1454i	0.540769	+	0.540769i	0.923754	−	0.382985i	$-0.125104\pi$
$163$	88.1454	+	88.1454i	0.540769	+	0.540769i	−0.382985	+	0.923754i	$0.625104\pi$
$164$	21.9732	+	26.1867i	0.133983	+	0.159675i
$165$		0			0
$166$	2.00305	−	11.3599i	0.0120666	−	0.0684329i
$167$	103.200	−	221.312i	0.617962	−	1.32522i	−0.309354	−	0.950947i	$-0.600113\pi$
$167$	103.200	−	221.312i	0.617962	−	1.32522i	0.927317	−	0.374278i	$-0.122109\pi$
$168$		0			0
$169$	−44.9835	+	7.93180i	−0.266174	+	0.0469337i
$170$	64.1488	−	39.7956i	0.377346	−	0.234092i
$171$		0			0
$172$	−18.9296	−	70.6463i	−0.110056	−	0.410734i
$173$	−56.9867	−	122.208i	−0.329403	−	0.706407i	0.669949	−	0.742407i	$-0.266316\pi$
$173$	−56.9867	−	122.208i	−0.329403	−	0.706407i	−0.999352	+	0.0360004i	$0.988538\pi$
$174$		0			0
$175$	−88.5322	+	13.4334i	−0.505898	+	0.0767620i
$176$	53.3740	+	44.7861i	0.303261	+	0.254467i
$177$		0			0
$178$	−91.4973	−	196.216i	−0.514030	−	1.10234i
$179$	−241.899	−	139.661i	−1.35139	−	0.780227i	−0.362949	−	0.931809i	$-0.618230\pi$
$179$	−241.899	−	139.661i	−1.35139	−	0.780227i	−0.988445	+	0.151582i	$0.951563\pi$
$180$		0			0
$181$	54.3285	+	94.0998i	0.300158	+	0.519888i	0.976171	−	0.217001i	$-0.0696274\pi$
$181$	54.3285	+	94.0998i	0.300158	+	0.519888i	−0.676014	+	0.736889i	$0.736294\pi$
$182$	−101.544	−	71.1020i	−0.557935	−	0.390670i
$183$		0			0
$184$	11.7741	+	32.3491i	0.0639897	+	0.175810i
$185$	66.2079	+	88.4570i	0.357881	+	0.478146i
$186$		0			0
$187$	1.95807	−	22.3808i	0.0104709	−	0.119683i
$188$	50.6866	+	50.6866i	0.269610	+	0.269610i
$189$		0			0
$190$	−11.6290	−	10.9151i	−0.0612054	−	0.0574476i
$191$	97.1273	−	81.4995i	0.508520	−	0.426699i	−0.352088	−	0.935967i	$-0.614528\pi$
$191$	97.1273	−	81.4995i	0.508520	−	0.426699i	0.860608	+	0.509268i	$0.170084\pi$
$192$		0			0
$193$	−74.9327	+	52.4685i	−0.388253	+	0.271857i	−0.751363	−	0.659889i	$-0.770603\pi$
$193$	−74.9327	+	52.4685i	−0.388253	+	0.271857i	0.363111	+	0.931746i	$0.381715\pi$
$194$	43.6276	+	119.866i	0.224885	+	0.617865i
$195$		0			0
$196$	9.92004	+	56.2594i	0.0506125	+	0.287038i
$197$	68.0511	+	18.2342i	0.345437	+	0.0925596i	0.427366	−	0.904079i	$-0.359441\pi$
$197$	68.0511	+	18.2342i	0.345437	+	0.0925596i	−0.0819292	+	0.996638i	$0.526108\pi$
$198$		0			0
$199$	214.694	+	123.954i	1.07886	+	0.622883i	0.930590	−	0.366064i	$-0.119295\pi$
$199$	214.694	+	123.954i	1.07886	+	0.622883i	0.148274	+	0.988946i	$0.452628\pi$
$200$	68.4861	+	125.467i	0.342431	+	0.627335i
$201$		0			0
$202$	204.905	−	17.9269i	1.01438	−	0.0887468i
$203$	17.5616	+	200.730i	0.0865104	+	0.988818i
$204$		0			0
$205$	102.814	+	33.7759i	0.501533	+	0.164760i
$206$	−80.0383	+	138.630i	−0.388535	+	0.672963i
$207$		0			0
$208$	−75.1728	+	280.549i	−0.361408	+	1.34879i
$209$	−4.67442	+	0.824227i	−0.0223657	+	0.00394367i
$210$		0			0
$211$	291.396	−	106.059i	1.38102	−	0.502651i	0.458535	−	0.888676i	$-0.348374\pi$
$211$	291.396	−	106.059i	1.38102	−	0.502651i	0.922488	+	0.386025i	$0.126152\pi$
$212$	−65.4753	−	93.5084i	−0.308846	−	0.441077i
$213$		0			0
$214$	−278.829	−	332.296i	−1.30294	−	1.55279i
$215$	−168.824	−	158.459i	−0.785230	−	0.737020i
$216$		0			0
$217$	−21.3421	+	21.3421i	−0.0983509	+	0.0983509i
$218$	336.777	+	29.4642i	1.54485	+	0.135157i
$219$		0			0
$220$	−27.4736	−	3.95217i	−0.124880	−	0.0179644i
$221$	88.0047	−	32.0311i	0.398211	−	0.144937i
$222$		0			0
$223$	32.0347	−	45.7503i	0.143653	−	0.205158i	−0.740877	−	0.671641i	$-0.765590\pi$
$223$	32.0347	−	45.7503i	0.143653	−	0.205158i	0.884531	+	0.466482i	$0.154479\pi$
$224$	−74.3007	+	42.8975i	−0.331700	+	0.191507i
$225$		0			0
$226$	184.757	−	320.009i	0.817510	−	1.41597i
$227$	237.363	−	110.684i	1.04565	−	0.487596i	0.177619	−	0.984099i	$-0.443161\pi$
$227$	237.363	−	110.684i	1.04565	−	0.487596i	0.868035	+	0.496503i	$0.165383\pi$
$228$		0			0
$229$	−147.760	+	176.093i	−0.645240	+	0.768967i	−0.985188	−	0.171477i	$-0.945146\pi$
$229$	−147.760	+	176.093i	−0.645240	+	0.768967i	0.339948	+	0.940444i	$0.389590\pi$
$230$	−55.8917	−	43.9604i	−0.243008	−	0.191132i
$231$		0			0
$232$	291.513	−	135.935i	1.25652	−	0.585927i
$233$	303.670	−	81.3682i	1.30331	−	0.349220i	0.460606	−	0.887605i	$-0.347632\pi$
$233$	303.670	−	81.3682i	1.30331	−	0.349220i	0.842699	+	0.538385i	$0.180965\pi$
$234$		0			0
$235$	220.946	+	51.7656i	0.940195	+	0.220279i
$236$	23.0290	+	130.604i	0.0975806	+	0.553407i
$237$		0			0
$238$	49.0117	+	22.8545i	0.205932	+	0.0960275i
$239$	205.885	+	36.3030i	0.861443	+	0.151896i	0.586880	−	0.809674i	$-0.300356\pi$
$239$	205.885	+	36.3030i	0.861443	+	0.151896i	0.274562	+	0.961569i	$0.411467\pi$
$240$		0			0
$241$	77.9550	−	65.4120i	0.323465	−	0.271419i	−0.466566	−	0.884486i	$-0.654509\pi$
$241$	77.9550	−	65.4120i	0.323465	−	0.271419i	0.790031	+	0.613067i	$0.210065\pi$
$242$	181.465	−	181.465i	0.749853	−	0.749853i
$243$		0			0
$244$		−	150.146i		−	0.615351i
$245$	120.577	+	134.792i	0.492151	+	0.550171i
$246$		0			0
$247$	−11.3490	−	16.2080i	−0.0459472	−	0.0656195i
$248$	43.6660	+	20.3618i	0.176073	+	0.0821040i
$249$		0			0
$250$	−256.833	−	145.653i	−1.02733	−	0.582613i
$251$	81.4048	+	140.997i	0.324322	+	0.561742i	0.981375	−	0.192102i	$-0.0615306\pi$
$251$	81.4048	+	140.997i	0.324322	+	0.561742i	−0.657053	+	0.753844i	$0.728197\pi$
$252$		0			0
$253$	−20.4412	+	5.47720i	−0.0807952	+	0.0216490i
$254$	17.9140	−	49.2183i	0.0705276	−	0.193773i
$255$		0			0
$256$	200.848	+	168.531i	0.784561	+	0.658325i
$257$	−111.162	+	9.72540i	−0.432536	+	0.0378420i	−0.301345	−	0.953515i	$-0.597436\pi$
$257$	−111.162	+	9.72540i	−0.432536	+	0.0378420i	−0.131191	+	0.991357i	$0.541880\pi$
$258$		0			0
$259$	−27.0714	+	74.3780i	−0.104523	+	0.287174i
$260$	−33.4693	−	110.758i	−0.128728	−	0.425994i
$261$		0			0
$262$	−535.427	−	143.467i	−2.04362	−	0.547585i
$263$	173.306	−	247.506i	0.658957	−	0.941088i	−0.341043	−	0.940048i	$-0.610780\pi$
$263$	173.306	−	247.506i	0.658957	−	0.941088i	0.999999	−	0.00104015i	$-0.000331090\pi$
$264$		0			0
$265$	−332.195	−	142.283i	−1.25356	−	0.536917i
$266$	1.98399	−	11.2518i	0.00745861	−	0.0422999i
$267$		0			0
$268$	115.226	+	10.0810i	0.429949	+	0.0376156i
$269$			119.721i			0.445060i	0.974926	+	0.222530i	$0.0714315\pi$
$269$			119.721i			0.445060i	−0.974926	+	0.222530i	$0.928568\pi$
$270$		0			0
$271$	−141.433			−0.521894			−0.260947	−	0.965353i	$-0.584035\pi$
$271$	−141.433			−0.521894			−0.260947	+	0.965353i	$0.584035\pi$
$272$	11.0432	−	126.224i	0.0405999	−	0.464059i
$273$		0			0
$274$	−53.6583	−	9.46140i	−0.195833	−	0.0345307i
$275$	−80.5044	+	35.2182i	−0.292743	+	0.128066i
$276$		0			0
$277$	−25.4895	−	17.8479i	−0.0920198	−	0.0644329i	0.526661	−	0.850075i	$-0.323444\pi$
$277$	−25.4895	−	17.8479i	−0.0920198	−	0.0644329i	−0.618681	+	0.785642i	$0.712333\pi$
$278$	86.7567	−	323.780i	0.312074	−	1.16468i
$279$		0			0
$280$	−48.3664	+	90.2558i	−0.172737	+	0.322342i
$281$	193.860	+	70.5593i	0.689894	+	0.251101i	0.663090	−	0.748540i	$-0.269245\pi$
$281$	193.860	+	70.5593i	0.689894	+	0.251101i	0.0268039	+	0.999641i	$0.491467\pi$
$282$		0			0
$283$	2.87663	+	32.8800i	0.0101648	+	0.116184i	0.999582	−	0.0289155i	$-0.00920537\pi$
$283$	2.87663	+	32.8800i	0.0101648	+	0.116184i	−0.989417	+	0.145099i	$0.953650\pi$
$284$	−56.4497	+	67.2742i	−0.198767	+	0.236881i
$285$		0			0
$286$	−114.308	−	41.6047i	−0.399679	−	0.145471i
$287$	20.0650	+	74.8834i	0.0699127	+	0.260918i
$288$		0			0
$289$	214.899	−	124.072i	0.743596	−	0.429315i
$290$	−363.664	+	556.032i	−1.25401	+	1.91735i
$291$		0			0
$292$	89.7287	−	192.424i	0.307290	−	0.658986i
$293$	−106.365	+	74.4778i	−0.363022	+	0.254190i	−0.740829	−	0.671694i	$-0.765567\pi$
$293$	−106.365	+	74.4778i	−0.363022	+	0.254190i	0.377807	+	0.925884i	$0.376678\pi$
$294$		0			0
$295$	279.915	+	312.915i	0.948865	+	1.06073i
$296$	126.349			0.426856
$297$		0			0
$298$	−351.525	−	351.525i	−1.17962	−	1.17962i
$299$	−56.7046	−	67.5779i	−0.189648	−	0.226013i
$300$		0			0
$301$	28.8026	−	163.348i	0.0956897	−	0.542683i
$302$	252.858	−	542.255i	0.837277	−	1.79555i
$303$		0			0
$304$	−26.3630	+	4.64851i	−0.0867203	+	0.0152911i
$305$	−250.576	−	403.917i	−0.821560	−	1.32432i
$306$		0			0
$307$	−109.109	−	407.200i	−0.355404	−	1.32639i	−0.879975	−	0.475019i	$-0.842441\pi$
$307$	−109.109	−	407.200i	−0.355404	−	1.32639i	0.524571	−	0.851366i	$-0.324226\pi$
$308$	−8.40321	−	18.0207i	−0.0272832	−	0.0585089i
$309$		0			0
$310$	−98.8175	+	11.8077i	−0.318766	+	0.0380893i
$311$	331.968	+	278.554i	1.06742	+	0.895672i	0.994816	−	0.101689i	$-0.0324247\pi$
$311$	331.968	+	278.554i	1.06742	+	0.895672i	0.0726038	+	0.997361i	$0.476869\pi$
$312$		0			0
$313$	228.281	+	489.550i	0.729332	+	1.56406i	0.822732	+	0.568429i	$0.192449\pi$
$313$	228.281	+	489.550i	0.729332	+	1.56406i	−0.0934003	+	0.995629i	$0.529774\pi$
$314$	−179.970	−	103.906i	−0.573154	−	0.330911i
$315$		0			0
$316$	29.5812	+	51.2361i	0.0936113	+	0.162140i
$317$	271.226	+	189.915i	0.855603	+	0.599100i	0.916944	−	0.399017i	$-0.130649\pi$
$317$	271.226	+	189.915i	0.855603	+	0.599100i	−0.0613401	+	0.998117i	$0.519537\pi$
$318$		0			0
$319$	67.6271	+	185.804i	0.211997	+	0.582457i
$320$	112.412	+	16.1709i	0.351288	+	0.0505340i
$321$		0			0
$322$	4.43967	−	50.7457i	0.0137878	−	0.157595i
$323$	6.10357	+	6.10357i	0.0188965	+	0.0188965i
$324$		0			0
$325$	−274.881	−	242.103i	−0.845789	−	0.744931i
$326$	−225.560	+	189.267i	−0.691901	+	0.580574i
$327$		0			0
$328$	101.373	−	70.9819i	0.309063	−	0.216408i
$329$	55.6001	+	152.760i	0.168997	+	0.464316i
$330$		0			0
$331$	−38.9001	−	220.613i	−0.117523	−	0.666505i	−0.985470	−	0.169849i	$-0.945672\pi$
$331$	−38.9001	−	220.613i	−0.117523	−	0.666505i	0.867947	−	0.496656i	$-0.165439\pi$
$332$	7.45007	+	1.99624i	0.0224400	+	0.00601277i
$333$		0			0
$334$	499.521	+	288.399i	1.49557	+	0.863469i
$335$	326.803	−	165.180i	0.975530	−	0.493074i
$336$		0			0
$337$	−154.344	+	13.5034i	−0.457996	+	0.0400694i	−0.313820	−	0.949483i	$-0.601609\pi$
$337$	−154.344	+	13.5034i	−0.457996	+	0.0400694i	−0.144176	+	0.989552i	$0.546053\pi$
$338$	−9.40353	−	107.483i	−0.0278211	−	0.317996i
$339$		0			0
$340$	22.7695	+	45.0486i	0.0669691	+	0.132496i
$341$	−14.8089	+	25.6498i	−0.0434279	+	0.0752194i
$342$		0			0
$343$	−78.9568	+	294.671i	−0.230195	+	0.859099i
$344$	−260.752	+	45.9776i	−0.757999	+	0.133656i
$345$		0			0
$346$	299.298	−	108.936i	0.865024	−	0.314843i
$347$	−155.096	−	221.500i	−0.446962	−	0.638328i	0.530935	−	0.847412i	$-0.321841\pi$
$347$	−155.096	−	221.500i	−0.446962	−	0.638328i	−0.977898	+	0.209084i	$0.932952\pi$
$348$		0			0
$349$	84.5706	+	100.787i	0.242323	+	0.288789i	0.873474	−	0.486871i	$-0.161862\pi$
$349$	84.5706	+	100.787i	0.242323	+	0.288789i	−0.631151	+	0.775660i	$0.717417\pi$
$350$	−13.3838	−	211.089i	−0.0382395	−	0.603112i
$351$		0			0
$352$	−59.5316	+	59.5316i	−0.169124	+	0.169124i
$353$	−560.875	−	49.0702i	−1.58888	−	0.139009i	−0.741855	−	0.670561i	$-0.766054\pi$
$353$	−560.875	−	49.0702i	−1.58888	−	0.139009i	−0.847026	+	0.531552i	$0.821609\pi$
$354$		0			0
$355$	−39.5867	+	275.187i	−0.111512	+	0.775176i
$356$	136.032	−	49.5116i	0.382112	−	0.139077i
$357$		0			0
$358$	378.433	−	540.458i	1.05707	−	1.50966i
$359$	−8.33750	+	4.81366i	−0.0232242	+	0.0134085i	−0.511567	−	0.859243i	$-0.670935\pi$
$359$	−8.33750	+	4.81366i	−0.0232242	+	0.0134085i	0.488343	+	0.872652i	$0.337602\pi$
$360$		0			0
$361$	−179.588	+	311.056i	−0.497474	+	0.861651i
$362$	−232.609	+	108.467i	−0.642567	+	0.299634i
$363$		0			0
$364$	53.2786	−	63.4950i	0.146370	−	0.174437i
$365$	−79.7475	−	667.400i	−0.218486	−	1.82849i
$366$		0			0
$367$	374.566	−	174.663i	1.02062	−	0.475921i	0.161051	−	0.986946i	$-0.448512\pi$
$367$	374.566	−	174.663i	1.02062	−	0.475921i	0.859566	+	0.511025i	$0.170734\pi$
$368$	−115.285	+	30.8905i	−0.313274	+	0.0839416i
$369$		0			0
$370$	−221.777	+	137.582i	−0.599397	+	0.371844i
$371$	−44.9544	−	254.949i	−0.121171	−	0.687194i
$372$		0			0
$373$	−86.4264	−	40.3013i	−0.231706	−	0.108046i	0.303298	−	0.952896i	$-0.401912\pi$
$373$	−86.4264	−	40.3013i	−0.231706	−	0.108046i	−0.535004	+	0.844849i	$0.679690\pi$
$374$	52.2608	+	9.21499i	0.139735	+	0.0246390i
$375$		0			0
$376$	198.789	−	166.804i	0.528694	−	0.443627i
$377$	−582.831	+	582.831i	−1.54597	+	1.54597i
$378$		0			0
$379$		−	597.153i		−	1.57560i	−0.615931	−	0.787800i	$-0.711220\pi$
$379$		−	597.153i		−	1.57560i	0.615931	−	0.787800i	$-0.288780\pi$
$380$	7.94821	−	7.11000i	0.0209163	−	0.0187105i
$381$		0			0
$382$	171.780	+	245.327i	0.449685	+	0.642217i
$383$	−248.482	−	115.869i	−0.648778	−	0.302530i	0.0702309	−	0.997531i	$-0.477626\pi$
$383$	−248.482	−	115.869i	−0.648778	−	0.302530i	−0.719009	+	0.695000i	$0.755404\pi$
$384$		0			0
$385$	−52.6807	−	34.4549i	−0.136833	−	0.0894933i
$386$	−108.036	−	187.125i	−0.279887	−	0.484779i
$387$		0			0
$388$	−82.3851	+	22.0750i	−0.212333	+	0.0568944i
$389$	−51.2144	+	140.710i	−0.131657	+	0.361724i	−0.987952	−	0.154764i	$-0.950538\pi$
$389$	−51.2144	+	140.710i	−0.131657	+	0.361724i	0.856295	+	0.516487i	$0.172761\pi$
$390$		0			0
$391$	29.4808	+	24.7373i	0.0753984	+	0.0632667i
$392$	206.024	−	18.0248i	0.525572	−	0.0459816i
$393$		0			0
$394$	−56.9162	+	156.376i	−0.144457	+	0.396894i
$395$	165.086	+	88.4664i	0.417938	+	0.223966i
$396$		0			0
$397$	−408.658	−	109.500i	−1.02937	−	0.275818i	−0.295666	−	0.955291i	$-0.595542\pi$
$397$	−408.658	−	109.500i	−1.02937	−	0.275818i	−0.733700	+	0.679473i	$0.762208\pi$
$398$	−335.872	+	479.675i	−0.843899	+	1.20521i
$399$		0			0
$400$	−454.032	+	198.625i	−1.13508	+	0.496562i
$401$	99.4097	−	563.780i	0.247904	−	1.40594i	−0.565745	−	0.824580i	$-0.691411\pi$
$401$	99.4097	−	563.780i	0.247904	−	1.40594i	0.813650	−	0.581356i	$-0.197477\pi$
$402$		0			0
$403$	−122.995	−	10.7606i	−0.305198	−	0.0267013i
$404$			137.532i			0.340425i
$405$		0			0
$406$	−475.950			−1.17229
$407$	−6.76948	+	77.3755i	−0.0166326	+	0.190112i
$408$		0			0
$409$	198.382	+	34.9800i	0.485041	+	0.0855257i	0.410821	−	0.911716i	$-0.365242\pi$
$409$	198.382	+	34.9800i	0.485041	+	0.0855257i	0.0742199	+	0.997242i	$0.476353\pi$
$410$	−100.644	+	234.977i	−0.245472	+	0.573115i
$411$		0			0
$412$	−87.6773	−	61.3923i	−0.212809	−	0.149010i
$413$	−77.8426	+	290.513i	−0.188481	+	0.703420i
$414$		0			0
$415$	23.3735	−	7.06308i	0.0563216	−	0.0170195i
$416$	−329.790	−	120.034i	−0.792764	−	0.288542i
$417$		0			0
$418$	−0.977160	−	11.1690i	−0.00233770	−	0.0267201i
$419$	139.993	−	166.838i	0.334113	−	0.398180i	−0.572664	−	0.819790i	$-0.694090\pi$
$419$	139.993	−	166.838i	0.334113	−	0.398180i	0.906778	+	0.421609i	$0.138535\pi$
$420$		0			0
$421$	−398.010	−	144.864i	−0.945392	−	0.344094i	−0.177099	−	0.984193i	$-0.556671\pi$
$421$	−398.010	−	144.864i	−0.945392	−	0.344094i	−0.768293	+	0.640099i	$0.778893\pi$
$422$	189.578	+	707.513i	0.449236	+	1.67657i
$423$		0			0
$424$	−357.888	+	206.627i	−0.844076	+	0.487327i
$425$	136.435	+	83.1890i	0.321023	+	0.195739i
$426$		0			0
$427$	143.905	−	308.606i	0.337015	−	0.722730i
$428$	237.591	−	166.363i	0.555120	−	0.388699i
$429$		0			0
$430$	407.624	−	364.636i	0.947962	−	0.847991i
$431$	222.552			0.516362			0.258181	−	0.966097i	$-0.416877\pi$
$431$	222.552			0.516362			0.258181	+	0.966097i	$0.416877\pi$
$432$		0			0
$433$	−280.953	−	280.953i	−0.648851	−	0.648851i	0.303864	−	0.952715i	$-0.401723\pi$
$433$	−280.953	−	280.953i	−0.648851	−	0.648851i	−0.952715	+	0.303864i	$0.901723\pi$
$434$	−45.8262	−	54.6135i	−0.105590	−	0.125838i
$435$		0			0
$436$	−39.2522	+	222.610i	−0.0900279	+	0.510573i
$437$	3.43620	−	7.36895i	0.00786315	−	0.0168626i
$438$		0			0
$439$	−89.7832	+	15.8312i	−0.204518	+	0.0360620i	−0.274968	−	0.961453i	$-0.588667\pi$
$439$	−89.7832	+	15.8312i	−0.204518	+	0.0360620i	0.0704507	+	0.997515i	$0.477556\pi$
$440$	−22.9216	+	97.8339i	−0.0520945	+	0.222350i
$441$		0			0
$442$	57.2545	+	213.677i	0.129535	+	0.483431i
$443$	208.641	+	447.431i	0.470972	+	1.01000i	0.988060	+	0.154070i	$0.0492382\pi$
$443$	208.641	+	447.431i	0.470972	+	1.01000i	−0.517088	+	0.855932i	$0.672984\pi$
$444$		0			0
$445$	283.320	−	360.216i	0.636675	−	0.809475i
$446$	101.059	+	84.7989i	0.226590	+	0.190132i
$447$		0			0
$448$	34.3830	+	73.7345i	0.0767477	+	0.164586i
$449$	−221.384	−	127.816i	−0.493061	−	0.284669i	0.232783	−	0.972529i	$-0.425217\pi$
$449$	−221.384	−	127.816i	−0.493061	−	0.284669i	−0.725843	+	0.687860i	$0.758550\pi$
$450$		0			0
$451$	38.0375	+	65.8829i	0.0843404	+	0.146082i
$452$	202.391	+	141.716i	0.447768	+	0.313530i
$453$		0			0
$454$	211.584	+	581.322i	0.466044	+	1.28045i
$455$	37.3629	−	259.728i	0.0821162	−	0.570832i
$456$		0			0
$457$	−44.4391	+	507.942i	−0.0972410	+	1.11147i	0.778158	+	0.628069i	$0.216154\pi$
$457$	−44.4391	+	507.942i	−0.0972410	+	1.11147i	−0.875399	+	0.483401i	$0.839401\pi$
$458$	−383.943	−	383.943i	−0.838304	−	0.838304i
$459$		0			0
$460$	32.5392	−	34.6676i	0.0707374	−	0.0753644i
$461$	−180.017	+	151.052i	−0.390492	+	0.327661i	−0.816805	−	0.576914i	$-0.804257\pi$
$461$	−180.017	+	151.052i	−0.390492	+	0.327661i	0.426313	+	0.904576i	$0.359812\pi$
$462$		0			0
$463$	−110.063	+	77.0668i	−0.237717	+	0.166451i	−0.686365	−	0.727258i	$-0.740795\pi$
$463$	−110.063	+	77.0668i	−0.237717	+	0.166451i	0.448648	+	0.893709i	$0.351906\pi$
$464$	381.406	+	1047.90i	0.821995	+	2.25841i
$465$		0			0
$466$	128.950	+	731.312i	0.276717	+	1.56934i
$467$	−26.9991	−	7.23439i	−0.0578140	−	0.0154912i	0.229796	−	0.973239i	$-0.426194\pi$
$467$	−26.9991	−	7.23439i	−0.0578140	−	0.0154912i	−0.287610	+	0.957748i	$0.592861\pi$
$468$		0			0
$469$	227.171	+	131.157i	0.484374	+	0.279654i
$470$	−167.295	+	509.247i	−0.355946	+	1.08350i
$471$		0			0
$472$	478.278	−	41.8439i	1.01330	−	0.0886523i
$473$	−14.1859	−	162.146i	−0.0299914	−	0.342803i
$474$		0			0
$475$	9.51628	−	32.3918i	0.0200343	−	0.0681932i
$476$	−18.0796	+	31.3148i	−0.0379824	+	0.0657874i
$477$		0			0
$478$	−127.809	+	476.991i	−0.267383	+	0.997888i
$479$	397.592	−	70.1063i	0.830047	−	0.146360i	0.257548	−	0.966265i	$-0.417085\pi$
$479$	397.592	−	70.1063i	0.830047	−	0.146360i	0.572499	+	0.819906i	$0.305974\pi$
$480$		0			0
$481$	−304.252	+	110.739i	−0.632541	+	0.230226i
$482$	137.872	+	196.901i	0.286040	+	0.408508i
$483$		0			0
$484$	110.298	+	131.449i	0.227889	+	0.271588i
$485$	−184.790	+	196.877i	−0.381009	+	0.405932i
$486$		0			0
$487$	198.013	−	198.013i	0.406597	−	0.406597i	−0.473953	−	0.880550i	$-0.657173\pi$
$487$	198.013	−	198.013i	0.406597	−	0.406597i	0.880550	+	0.473953i	$0.157173\pi$
$488$	−541.486	−	47.3739i	−1.10960	−	0.0970776i
$489$		0			0
$490$	−342.000	+	255.979i	−0.697959	+	0.522405i
$491$	508.696	−	185.150i	1.03604	−	0.377088i	0.232663	−	0.972557i	$-0.425256\pi$
$491$	508.696	−	185.150i	1.03604	−	0.377088i	0.803378	+	0.595470i	$0.203034\pi$
$492$		0			0
$493$	206.244	−	294.548i	0.418346	−	0.597460i
$494$	40.4752	−	23.3684i	0.0819336	−	0.0473044i
$495$		0			0
$496$	−83.5199	+	144.661i	−0.168387	+	0.291655i
$497$	−180.504	+	84.1702i	−0.363186	+	0.169357i
$498$		0			0
$499$	−183.346	+	218.504i	−0.367427	+	0.437883i	−0.917804	−	0.397033i	$-0.870040\pi$
$499$	−183.346	+	218.504i	−0.367427	+	0.437883i	0.550377	+	0.834916i	$0.314484\pi$
$500$	111.987	−	162.588i	0.223974	−	0.325176i
$501$		0			0
$502$	−348.537	+	162.525i	−0.694297	+	0.323756i
$503$	793.904	−	212.726i	1.57834	−	0.422914i	0.639927	−	0.768435i	$-0.278964\pi$
$503$	793.904	−	212.726i	1.57834	−	0.422914i	0.938411	+	0.345521i	$0.112298\pi$
$504$		0			0
$505$	229.525	+	369.984i	0.454505	+	0.732642i
$506$	−8.68012	−	49.2274i	−0.0171544	−	0.0972874i
$507$		0			0
$508$	31.7404	+	14.8008i	0.0624810	+	0.0291354i
$509$	−460.147	−	81.1364i	−0.904022	−	0.159403i	−0.297734	−	0.954649i	$-0.596231\pi$
$509$	−460.147	−	81.1364i	−0.904022	−	0.159403i	−0.606288	+	0.795245i	$0.707342\pi$
$510$		0			0
$511$	368.853	−	309.504i	0.721825	−	0.605683i
$512$	−15.1697	+	15.1697i	−0.0296284	+	0.0296284i
$513$		0			0
$514$		−	263.575i		−	0.512792i
$515$	−338.324	−	18.8326i	−0.656940	−	0.0365682i
$516$		0			0
$517$	91.4989	+	130.674i	0.176980	+	0.252754i
$518$	−169.445	−	79.0133i	−0.327113	−	0.152535i
$519$		0			0
$520$	−410.000	+	85.7576i	−0.788461	+	0.164919i
$521$	−113.109	−	195.911i	−0.217100	−	0.376029i	0.736820	−	0.676089i	$-0.236327\pi$
$521$	−113.109	−	195.911i	−0.217100	−	0.376029i	−0.953920	+	0.300060i	$0.902993\pi$
$522$		0			0
$523$	−1.77194	+	0.474790i	−0.00338803	+	0.000907820i	−0.260513	−	0.965470i	$-0.583892\pi$
$523$	−1.77194	+	0.474790i	−0.00338803	+	0.000907820i	0.257125	+	0.966378i	$0.417225\pi$
$524$	126.766	−	348.287i	0.241920	−	0.664671i
$525$		0			0
$526$	546.725	+	458.756i	1.03940	+	0.872161i
$527$	53.6562	−	4.69431i	0.101814	−	0.00890761i
$528$		0			0
$529$	−168.530	+	463.033i	−0.318583	+	0.875299i
$530$	403.192	−	752.391i	0.760740	−	1.41960i
$531$		0			0
$532$	7.37918	+	1.97725i	0.0138706	+	0.00371663i
$533$	−181.896	+	259.774i	−0.341268	+	0.487381i
$534$		0			0
$535$	361.521	−	844.059i	0.675740	−	1.57768i
$536$	72.7123	−	412.372i	0.135657	−	0.769351i
$537$		0			0
$538$	−281.714	−	24.6468i	−0.523632	−	0.0458118i
$539$			127.133i			0.235869i
$540$		0			0
$541$	−234.130			−0.432773			−0.216386	−	0.976308i	$-0.569427\pi$
$541$	−234.130			−0.432773			−0.216386	+	0.976308i	$0.569427\pi$
$542$	29.1166	−	332.804i	0.0537207	−	0.614030i
$543$		0			0
$544$	150.777	+	26.5861i	0.277164	+	0.0488716i
$545$	265.915	+	664.367i	0.487918	+	1.21902i
$546$		0			0
$547$	264.852	+	185.452i	0.484191	+	0.339034i	0.790050	−	0.613043i	$-0.210055\pi$
$547$	264.852	+	185.452i	0.484191	+	0.339034i	−0.305859	+	0.952077i	$0.598944\pi$
$548$	9.42924	−	35.1904i	0.0172066	−	0.0642160i
$549$		0			0
$550$	−66.2981	−	196.684i	−0.120542	−	0.357607i
$551$	−71.3874	−	25.9829i	−0.129560	−	0.0471559i
$552$		0			0
$553$	11.6938	+	133.661i	0.0211462	+	0.241702i
$554$	47.2451	−	56.3045i	0.0852800	−	0.101633i
$555$		0			0
$556$	210.614	+	76.6573i	0.378803	+	0.137873i
$557$	1.77258	+	6.61538i	0.00318238	+	0.0118768i	0.967499	−	0.252876i	$-0.0813764\pi$
$557$	1.77258	+	6.61538i	0.00318238	+	0.0118768i	−0.964316	+	0.264753i	$0.914710\pi$
$558$		0			0
$559$	587.599	−	339.250i	1.05116	−	0.606888i
$560$	−297.110	−	194.320i	−0.530554	−	0.347000i
$561$		0			0
$562$	−205.942	+	441.643i	−0.366444	+	0.785842i
$563$	−517.684	+	362.486i	−0.919510	+	0.643847i	−0.934470	−	0.356041i	$-0.884126\pi$
$563$	−517.684	+	362.486i	−0.919510	+	0.643847i	0.0149610	+	0.999888i	$0.495238\pi$
$564$		0			0
$565$	780.974	+	43.4724i	1.38225	+	0.0769424i
$566$	−77.9617			−0.137742
$567$		0			0
$568$	224.807	+	224.807i	0.395787	+	0.395787i
$569$	76.5081	+	91.1789i	0.134461	+	0.160244i	0.829073	−	0.559140i	$-0.188869\pi$
$569$	76.5081	+	91.1789i	0.134461	+	0.160244i	−0.694613	+	0.719384i	$0.744424\pi$
$570$		0			0
$571$	0.263528	−	1.49454i	0.000461520	−	0.00261741i	−0.984576	−	0.174957i	$-0.944021\pi$
$571$	0.263528	−	1.49454i	0.000461520	−	0.00261741i	0.985038	+	0.172339i	$0.0551326\pi$
$572$	34.3743	−	73.7160i	0.0600950	−	0.128874i
$573$		0			0
$574$	−180.338	+	31.7984i	−0.314177	+	0.0553979i
$575$	29.6798	−	147.566i	0.0516170	−	0.256637i
$576$		0			0
$577$	108.806	+	406.071i	0.188573	+	0.703763i	0.993837	+	0.110847i	$0.0353565\pi$
$577$	108.806	+	406.071i	0.188573	+	0.703763i	−0.805265	+	0.592915i	$0.797977\pi$
$578$	247.711	+	531.218i	0.428566	+	0.919063i
$579$		0			0
$580$	−349.180	−	274.640i	−0.602034	−	0.473517i
$581$	13.3994	+	11.2435i	0.0230627	+	0.0193519i
$582$		0			0
$583$	−107.362	−	230.239i	−0.184154	−	0.394921i
$584$	−665.647	−	384.312i	−1.13981	−	0.658068i
$585$		0			0
$586$	−153.355	−	265.619i	−0.261698	−	0.453275i
$587$	−246.684	−	172.730i	−0.420246	−	0.294259i	0.344262	−	0.938874i	$-0.388129\pi$
$587$	−246.684	−	172.730i	−0.420246	−	0.294259i	−0.764508	+	0.644614i	$0.777018\pi$
$588$		0			0
$589$	−3.89200	−	10.6932i	−0.00660781	−	0.0181548i
$590$	−793.941	+	594.245i	−1.34566	+	1.00720i
$591$		0			0
$592$	−38.1788	+	436.385i	−0.0644911	+	0.737137i
$593$	31.7465	+	31.7465i	0.0535355	+	0.0535355i	0.733368	−	0.679832i	$-0.237947\pi$
$593$	31.7465	+	31.7465i	0.0535355	+	0.0535355i	−0.679832	+	0.733368i	$0.737947\pi$
$594$		0			0
$595$	3.62353	+	114.415i	0.00608997	+	0.192294i
$596$	254.637	−	213.665i	0.427243	−	0.358499i
$597$		0			0
$598$	170.690	−	119.519i	0.285435	−	0.199864i
$599$	16.1057	+	44.2501i	0.0268877	+	0.0738734i	0.952410	−	0.304819i	$-0.0985960\pi$
$599$	16.1057	+	44.2501i	0.0268877	+	0.0738734i	−0.925523	+	0.378693i	$0.876374\pi$
$600$		0			0
$601$	160.281	+	908.998i	0.266690	+	1.51248i	0.764179	+	0.645005i	$0.223145\pi$
$601$	160.281	+	908.998i	0.266690	+	1.51248i	−0.497489	+	0.867471i	$0.665744\pi$
$602$	378.441	+	101.403i	0.628640	+	0.168443i
$603$		0			0
$604$	346.460	+	200.029i	0.573610	+	0.331174i
$605$	516.094	+	169.544i	0.853049	+	0.280238i
$606$		0			0
$607$	−134.360	+	11.7550i	−0.221351	+	0.0193657i	−0.197291	−	0.980345i	$-0.563215\pi$
$607$	−134.360	+	11.7550i	−0.221351	+	0.0193657i	−0.0240591	+	0.999711i	$0.507659\pi$
$608$	−2.81920	−	32.2236i	−0.00463684	−	0.0529994i
$609$		0			0
$610$	1002.04	−	506.472i	1.64268	−	0.830282i
$611$	−332.493	+	575.896i	−0.544179	+	0.942546i
$612$		0			0
$613$	193.130	−	720.773i	0.315058	−	1.17581i	−0.608878	−	0.793264i	$-0.708380\pi$
$613$	193.130	−	720.773i	0.315058	−	1.17581i	0.923936	−	0.382548i	$-0.124953\pi$
$614$	980.639	−	172.913i	1.59713	−	0.281617i
$615$		0			0
$616$	−67.6415	+	24.6195i	−0.109808	+	0.0399667i
$617$	−277.352	−	396.100i	−0.449518	−	0.641978i	0.528883	−	0.848695i	$-0.322611\pi$
$617$	−277.352	−	396.100i	−0.449518	−	0.641978i	−0.978401	+	0.206717i	$0.933722\pi$
$618$		0			0
$619$	−710.594	−	846.852i	−1.14797	−	1.36810i	−0.918806	−	0.394710i	$-0.870845\pi$
$619$	−710.594	−	846.852i	−1.14797	−	1.36810i	−0.229164	−	0.973388i	$-0.573599\pi$
$620$	−2.10639	−	66.5104i	−0.00339740	−	0.107275i
$621$		0			0
$622$	−723.802	+	723.802i	−1.16367	+	1.16367i
$623$	327.051	+	28.6132i	0.524961	+	0.0459281i
$624$		0			0
$625$	29.9230	−	624.283i	0.0478768	−	0.998853i
$626$	−1198.95	+	436.381i	−1.91525	+	0.697095i
$627$		0			0
$628$	79.6997	−	113.823i	0.126910	−	0.181247i
$629$	122.324	−	70.6239i	0.194474	−	0.112280i
$630$		0			0
$631$	468.867	−	812.101i	0.743054	−	1.28701i	−0.208045	−	0.978119i	$-0.566710\pi$
$631$	468.867	−	812.101i	0.743054	−	1.28701i	0.951099	−	0.308887i	$-0.0999566\pi$
$632$	194.112	−	90.5158i	0.307139	−	0.143221i
$633$		0			0
$634$	−502.722	+	599.121i	−0.792937	+	0.944986i
$635$	110.088	−	13.1544i	0.173367	−	0.0207155i
$636$		0			0
$637$	−480.313	+	223.973i	−0.754023	+	0.351607i
$638$	−451.134	+	120.881i	−0.707107	+	0.189469i
$639$		0			0
$640$	−170.473	+	727.613i	−0.266364	+	1.13690i
$641$	−144.211	−	817.859i	−0.224977	−	1.27591i	−0.862728	−	0.505668i	$-0.831246\pi$
$641$	−144.211	−	817.859i	−0.224977	−	1.27591i	0.637751	−	0.770243i	$-0.279865\pi$
$642$		0			0
$643$	−492.087	−	229.464i	−0.765299	−	0.356865i	0.000453650	−	1.00000i	$-0.499856\pi$
$643$	−492.087	−	229.464i	−0.765299	−	0.356865i	−0.765753	+	0.643135i	$0.777633\pi$
$644$	33.5430	+	5.91453i	0.0520854	+	0.00918406i
$645$		0			0
$646$	−15.6187	+	13.1057i	−0.0241776	+	0.0202874i
$647$	396.580	−	396.580i	0.612952	−	0.612952i	−0.330762	−	0.943714i	$-0.607306\pi$
$647$	396.580	−	396.580i	0.612952	−	0.612952i	0.943714	+	0.330762i	$0.107306\pi$
$648$		0			0
$649$			295.136i			0.454755i
$650$	626.277	−	596.978i	0.963503	−	0.918427i
$651$		0			0
$652$	−112.926	−	161.275i	−0.173199	−	0.247355i
$653$	−190.492	−	88.8280i	−0.291719	−	0.136031i	0.271250	−	0.962509i	$-0.412563\pi$
$653$	−190.492	−	88.8280i	−0.291719	−	0.136031i	−0.562969	+	0.826478i	$0.690341\pi$
$654$		0			0
$655$	−240.228	−	1148.51i	−0.366761	−	1.75345i
$656$	214.526	+	371.569i	0.327021	+	0.566416i
$657$		0			0
$658$	−370.904	+	99.3833i	−0.563683	+	0.151038i
$659$	280.075	−	769.498i	0.424999	−	1.16768i	−0.523812	−	0.851834i	$-0.675491\pi$
$659$	280.075	−	769.498i	0.424999	−	1.16768i	0.948812	−	0.315842i	$-0.102287\pi$
$660$		0			0
$661$	−160.592	−	134.752i	−0.242952	−	0.203861i	0.513178	−	0.858282i	$-0.328468\pi$
$661$	−160.592	−	134.752i	−0.242952	−	0.203861i	−0.756130	+	0.654421i	$0.772912\pi$
$662$	527.130	−	46.1179i	0.796269	−	0.0696645i
$663$		0			0
$664$	9.54990	−	26.2381i	0.0143824	−	0.0395153i
$665$	23.1511	−	6.99587i	0.0348136	−	0.0105201i
$666$		0			0
$667$	−327.164	−	87.6634i	−0.490501	−	0.131429i
$668$	−221.213	+	315.924i	−0.331156	+	0.472940i
$669$		0			0
$670$	321.404	+	802.999i	0.479707	+	1.19851i
$671$	58.0228	−	329.064i	0.0864722	−	0.490408i
$672$		0			0
$673$	−1158.65	−	101.369i	−1.72162	−	0.150622i	−0.816943	−	0.576719i	$-0.804333\pi$
$673$	−1158.65	−	101.369i	−1.72162	−	0.150622i	−0.904678	+	0.426097i	$0.859888\pi$
$674$		−	365.965i		−	0.542975i
$675$		0			0
$676$	72.1423			0.106719
$677$	−97.9291	+	1119.33i	−0.144652	+	1.65337i	0.483545	+	0.875320i	$0.339349\pi$
$677$	−97.9291	+	1119.33i	−0.144652	+	1.65337i	−0.628196	+	0.778055i	$0.716206\pi$
$678$		0			0
$679$	−190.490	−	33.5885i	−0.280545	−	0.0494676i
$680$	169.648	−	67.9023i	0.249482	−	0.0998563i
$681$		0			0
$682$	−57.3075	−	40.1271i	−0.0840286	−	0.0588374i
$683$	−22.5930	+	84.3181i	−0.0330790	+	0.123453i	−0.980491	−	0.196564i	$-0.937022\pi$
$683$	−22.5930	+	84.3181i	−0.0330790	+	0.123453i	0.947412	+	0.320016i	$0.103688\pi$
$684$		0			0
$685$	−33.3624	−	110.405i	−0.0487043	−	0.161175i
$686$	−677.131	−	246.455i	−0.987071	−	0.359265i
$687$		0			0
$688$	−80.0063	−	914.477i	−0.116288	−	1.32918i
$689$	680.704	−	811.232i	0.987960	−	1.17740i
$690$		0			0
$691$	−890.562	−	324.138i	−1.28880	−	0.469086i	−0.395469	−	0.918479i	$-0.629418\pi$
$691$	−890.562	−	324.138i	−1.28880	−	0.469086i	−0.893334	+	0.449394i	$0.851640\pi$
$692$	55.1201	+	205.711i	0.0796533	+	0.297270i
$693$		0			0
$694$	553.137	−	319.354i	0.797028	−	0.460164i
$695$	694.521	−	145.269i	0.999311	−	0.209021i
$696$		0			0
$697$	58.4673	−	125.383i	0.0838842	−	0.179890i
$698$	−254.571	+	178.253i	−0.364716	+	0.255377i
$699$		0			0
$700$	141.386	+	3.38651i	0.201981	+	0.00483787i
$701$	−312.401			−0.445651			−0.222825	−	0.974858i	$-0.571528\pi$
$701$	−312.401			−0.445651			−0.222825	+	0.974858i	$0.571528\pi$
$702$		0			0
$703$	−21.1014	−	21.1014i	−0.0300162	−	0.0300162i
$704$	51.3172	+	61.1575i	0.0728938	+	0.0868714i
$705$		0			0
$706$	230.933	−	1309.68i	0.327100	−	1.85508i
$707$	−131.816	+	282.680i	−0.186444	+	0.399830i
$708$		0			0
$709$	837.243	−	147.629i	1.18088	−	0.208221i	0.451462	−	0.892290i	$-0.350903\pi$
$709$	837.243	−	147.629i	1.18088	−	0.208221i	0.729417	+	0.684069i	$0.239791\pi$
$710$	−639.389	−	149.803i	−0.900548	−	0.210990i
$711$		0			0
$712$	−135.638	−	506.208i	−0.190503	−	0.710966i
$713$	−21.4415	−	45.9814i	−0.0300722	−	0.0644901i
$714$		0			0
$715$	−30.5506	−	255.676i	−0.0427282	−	0.357588i
$716$	337.945	+	283.570i	0.471991	+	0.396047i
$717$		0			0
$718$	−9.61051	−	20.6098i	−0.0133851	−	0.0287045i
$719$	228.610	+	131.988i	0.317956	+	0.183572i	0.650481	−	0.759522i	$-0.274567\pi$
$719$	228.610	+	131.988i	0.317956	+	0.183572i	−0.332525	+	0.943094i	$0.607901\pi$
$720$		0			0
$721$	−121.369	−	210.218i	−0.168335	−	0.291564i
$722$	−694.969	−	486.623i	−0.962561	−	0.673992i
$723$		0			0
$724$	−58.6946	−	161.262i	−0.0810698	−	0.222738i
$725$	−1397.70	−	156.087i	−1.92786	−	0.215293i
$726$		0			0
$727$	−50.9264	+	582.092i	−0.0700501	+	0.800676i	0.877188	+	0.480146i	$0.159416\pi$
$727$	−50.9264	+	582.092i	−0.0700501	+	0.800676i	−0.947238	+	0.320530i	$0.896139\pi$
$728$	−212.178	−	212.178i	−0.291454	−	0.291454i
$729$		0			0
$730$	1586.87	−	50.2561i	2.17379	−	0.0688440i
$731$	−226.745	+	190.262i	−0.310185	+	0.260276i
$732$		0			0
$733$	−787.798	+	551.622i	−1.07476	+	0.752554i	−0.970283	−	0.241973i	$-0.922205\pi$
$733$	−787.798	+	551.622i	−1.07476	+	0.752554i	−0.104476	+	0.994527i	$0.533317\pi$
$734$	333.886	+	917.344i	0.454885	+	1.24979i
$735$		0			0
$736$	−25.0430	−	142.026i	−0.0340258	−	0.192970i
$737$	248.638	+	66.6223i	0.337365	+	0.0903967i
$738$		0			0
$739$	−625.369	−	361.057i	−0.846236	−	0.488575i	0.0131429	−	0.999914i	$-0.495816\pi$
$739$	−625.369	−	361.057i	−0.846236	−	0.488575i	−0.859379	+	0.511339i	$0.829150\pi$
$740$	−78.7192	−	155.743i	−0.106377	−	0.210464i
$741$		0			0
$742$	609.171	−	53.2956i	0.820986	−	0.0718269i
$743$	100.027	+	1143.31i	0.134626	+	1.53878i	0.700120	+	0.714025i	$0.253130\pi$
$743$	100.027	+	1143.31i	0.134626	+	1.53878i	−0.565494	+	0.824752i	$0.691315\pi$
$744$		0			0
$745$	328.433	−	999.756i	0.440850	−	1.34195i
$746$	112.625	−	195.072i	0.150972	−	0.261491i
$747$		0			0
$748$	−9.18367	+	34.2739i	−0.0122776	+	0.0458207i
$749$	647.789	−	114.223i	0.864872	−	0.152500i
$750$		0			0
$751$	1206.84	−	439.255i	1.60698	−	0.584894i	0.626142	−	0.779709i	$-0.284633\pi$
$751$	1206.84	−	439.255i	1.60698	−	0.584894i	0.980840	+	0.194815i	$0.0624106\pi$
$752$	516.039	+	736.980i	0.686222	+	0.980026i
$753$		0			0
$754$	−1251.46	−	1491.44i	−1.65977	−	1.97803i
$755$	1265.86	−	40.0899i	1.67664	−	0.0530992i
$756$		0			0
$757$	337.827	−	337.827i	0.446271	−	0.446271i	−0.447842	−	0.894113i	$-0.647807\pi$
$757$	337.827	−	337.827i	0.446271	−	0.446271i	0.894113	+	0.447842i	$0.147807\pi$
$758$	1405.15	+	122.935i	1.85376	+	0.162183i
$759$		0			0
$760$	−23.1337	−	30.9078i	−0.0304391	−	0.0406682i
$761$	684.518	−	249.144i	0.899497	−	0.327390i	0.149446	−	0.988770i	$-0.452251\pi$
$761$	684.518	−	249.144i	0.899497	−	0.327390i	0.750051	+	0.661380i	$0.230029\pi$
$762$		0			0
$763$	−294.036	+	419.927i	−0.385368	+	0.550363i
$764$	−173.423	+	100.126i	−0.226993	+	0.131055i
$765$		0			0
$766$	323.804	−	560.846i	0.422721	−	0.732174i
$767$	−1115.03	+	519.946i	−1.45375	+	0.677896i
$768$		0			0
$769$	−699.977	+	834.200i	−0.910243	+	1.08479i	0.0858349	+	0.996309i	$0.472644\pi$
$769$	−699.977	+	834.200i	−0.910243	+	1.08479i	−0.996078	+	0.0884764i	$0.971800\pi$
$770$	91.9206	−	116.869i	0.119377	−	0.151778i
$771$		0			0
$772$	130.940	−	61.0581i	0.169611	−	0.0790909i
$773$	−668.219	+	179.049i	−0.864449	+	0.231628i	−0.663686	−	0.748011i	$-0.731009\pi$
$773$	−668.219	+	179.049i	−0.864449	+	0.231628i	−0.200763	+	0.979640i	$0.564342\pi$
$774$		0			0
$775$	−116.665	−	175.409i	−0.150535	−	0.226334i
$776$	53.6174	+	304.079i	0.0690946	+	0.391855i
$777$		0			0
$778$	−320.560	−	149.480i	−0.412031	−	0.192133i
$779$	−28.7847	−	5.07551i	−0.0369508	−	0.00651542i
$780$		0			0
$781$	−149.715	+	125.626i	−0.191696	+	0.160852i
$782$	−64.2781	+	64.2781i	−0.0821970	+	0.0821970i
$783$		0			0
$784$			717.012i			0.914556i
$785$	24.4485	−	439.213i	0.0311446	−	0.559507i
$786$		0			0
$787$	−656.999	−	938.292i	−0.834815	−	1.19224i	−0.979236	−	0.202723i	$-0.935021\pi$
$787$	−656.999	−	938.292i	−0.834815	−	1.19224i	0.144421	−	0.989516i	$-0.453868\pi$
$788$	−100.845	−	47.0249i	−0.127976	−	0.0596763i
$789$		0			0
$790$	−242.155	+	370.248i	−0.306525	+	0.468668i
$791$	280.164	+	485.258i	0.354190	+	0.613475i
$792$		0			0
$793$	1345.43	−	360.507i	1.69663	−	0.454611i
$794$	341.792	−	939.065i	0.430468	−	1.18270i
$795$		0			0
$796$	−299.938	−	251.678i	−0.376807	−	0.316178i
$797$	−760.933	+	66.5730i	−0.954746	+	0.0835295i	−0.553870	−	0.832603i	$-0.686850\pi$
$797$	−760.933	+	66.5730i	−0.954746	+	0.0835295i	−0.400876	+	0.916132i	$0.631294\pi$
$798$		0			0
$799$	99.2198	−	272.604i	0.124180	−	0.341182i
$800$	−191.276	−	567.452i	−0.239095	−	0.709315i
$801$		0			0
$802$	1306.16	+	349.984i	1.62862	+	0.436389i
$803$	271.013	−	387.047i	0.337501	−	0.482002i
$804$		0			0
$805$	100.107	−	40.0683i	0.124357	−	0.0497742i
$806$	50.6414	−	287.202i	0.0628305	−	0.356329i
$807$		0			0
$808$	495.996	+	43.3940i	0.613856	+	0.0537054i
$809$		−	983.045i		−	1.21514i	−0.794267	−	0.607568i	$-0.792145\pi$
$809$		−	983.045i		−	1.21514i	0.794267	−	0.607568i	$-0.207855\pi$
$810$		0			0
$811$	1259.96			1.55358			0.776792	−	0.629757i	$-0.216845\pi$
$811$	1259.96			1.55358			0.776792	+	0.629757i	$0.216845\pi$
$812$	27.7366	−	317.030i	0.0341583	−	0.390431i
$813$		0			0
$814$	−180.677	−	31.8583i	−0.221962	−	0.0391380i
$815$	−572.940	−	245.397i	−0.702994	−	0.301101i
$816$		0			0
$817$	51.2264	+	35.8691i	0.0627006	+	0.0439034i
$818$	−123.151	+	459.607i	−0.150552	+	0.561867i
$819$		0			0
$820$	−150.653	−	80.7323i	−0.183723	−	0.0984540i
$821$	837.346	+	304.769i	1.01991	+	0.371217i	0.797230	−	0.603675i	$-0.206298\pi$
$821$	837.346	+	304.769i	1.01991	+	0.371217i	0.222679	+	0.974892i	$0.428520\pi$
$822$		0			0
$823$	−47.6180	−	544.277i	−0.0578591	−	0.661333i	−0.968644	−	0.248452i	$-0.920078\pi$
$823$	−47.6180	−	544.277i	−0.0578591	−	0.661333i	0.910785	−	0.412881i	$-0.135477\pi$
$824$	−249.070	+	296.830i	−0.302269	+	0.360230i
$825$		0			0
$826$	−667.575	−	242.978i	−0.808203	−	0.294162i
$827$	−99.0791	−	369.768i	−0.119805	−	0.447120i	0.879796	−	0.475351i	$-0.157679\pi$
$827$	−99.0791	−	369.768i	−0.119805	−	0.447120i	−0.999601	+	0.0282316i	$0.991012\pi$
$828$		0			0
$829$	−272.496	+	157.326i	−0.328705	+	0.189778i	−0.655266	−	0.755398i	$-0.727443\pi$
$829$	−272.496	+	157.326i	−0.328705	+	0.189778i	0.326561	+	0.945176i	$0.394110\pi$
$830$	11.8082	+	56.4538i	0.0142267	+	0.0680167i
$831$		0			0
$832$	−140.648	+	301.620i	−0.169048	+	0.362524i
$833$	189.385	−	132.609i	0.227353	−	0.159195i
$834$		0			0
$835$	−67.8588	+	1219.07i	−0.0812680	+	1.45996i
$836$	7.49661			0.00896724
$837$		0			0
$838$	363.763	+	363.763i	0.434084	+	0.434084i
$839$	156.428	+	186.423i	0.186446	+	0.222197i	0.851168	−	0.524893i	$-0.175895\pi$
$839$	156.428	+	186.423i	0.186446	+	0.222197i	−0.664723	+	0.747090i	$0.731450\pi$
$840$		0			0
$841$	−403.501	+	2288.37i	−0.479787	+	2.72101i
$842$	422.814	−	906.728i	0.502155	−	1.07687i
$843$		0			0
$844$	−482.322	+	85.0465i	−0.571472	+	0.100766i
$845$	194.075	−	120.397i	0.229675	−	0.142482i
$846$		0			0
$847$	100.720	+	375.891i	0.118913	+	0.443791i
$848$	−605.505	−	1298.51i	−0.714038	−	1.53126i
$849$		0			0
$850$	−223.838	+	303.917i	−0.263339	+	0.357549i
$851$	−101.922	−	85.5224i	−0.119767	−	0.100496i
$852$		0			0
$853$	543.503	+	1165.55i	0.637167	+	1.36641i	0.914088	+	0.405516i	$0.132908\pi$
$853$	543.503	+	1165.55i	0.637167	+	1.36641i	−0.276921	+	0.960893i	$0.589314\pi$
$854$	696.550	+	402.153i	0.815632	+	0.470905i
$855$		0			0
$856$	−525.009	−	909.342i	−0.613328	−	1.06232i
$857$	−778.374	−	545.023i	−0.908254	−	0.635967i	0.0232370	−	0.999730i	$-0.492603\pi$
$857$	−778.374	−	545.023i	−0.908254	−	0.635967i	−0.931491	+	0.363763i	$0.881492\pi$
$858$		0			0
$859$	162.636	+	446.840i	0.189332	+	0.520186i	0.997647	−	0.0685649i	$-0.0218420\pi$
$859$	162.636	+	446.840i	0.189332	+	0.520186i	−0.808314	+	0.588751i	$0.799620\pi$
$860$	219.129	+	292.768i	0.254802	+	0.340428i
$861$		0			0
$862$	−45.8164	+	523.684i	−0.0531513	+	0.607522i
$863$	1127.92	+	1127.92i	1.30698	+	1.30698i	0.923583	+	0.383398i	$0.125246\pi$
$863$	1127.92	+	1127.92i	1.30698	+	1.30698i	0.383398	+	0.923583i	$0.374754\pi$
$864$		0			0
$865$	491.590	+	461.409i	0.568313	+	0.533421i
$866$	718.944	−	603.266i	0.830189	−	0.696612i
$867$		0			0
$868$	39.0486	−	27.3422i	0.0449869	−	0.0315002i
$869$	45.0312	+	123.722i	0.0518196	+	0.142373i
$870$		0			0
$871$	186.330	+	1056.73i	0.213926	+	1.21324i
$872$	790.437	+	211.797i	0.906465	+	0.242887i
$873$		0			0
$874$	16.6323	+	9.60269i	0.0190301	+	0.0109871i
$875$	386.006	−	226.848i	0.441150	−	0.259254i
$876$		0			0
$877$	−308.611	+	27.0000i	−0.351894	+	0.0307868i	−0.261733	−	0.965140i	$-0.584294\pi$
$877$	−308.611	+	27.0000i	−0.351894	+	0.0307868i	−0.0901616	+	0.995927i	$0.528738\pi$
$878$	−18.7686	−	214.527i	−0.0213766	−	0.244336i
$879$		0			0
$880$	−330.972	−	108.729i	−0.376105	−	0.123555i
$881$	−253.650	+	439.334i	−0.287911	+	0.498677i	−0.973311	−	0.229490i	$-0.926294\pi$
$881$	−253.650	+	439.334i	−0.287911	+	0.498677i	0.685400	+	0.728167i	$0.259627\pi$
$882$		0			0
$883$	−164.139	+	612.574i	−0.185888	+	0.693742i	0.808551	+	0.588426i	$0.200252\pi$
$883$	−164.139	+	612.574i	−0.185888	+	0.693742i	−0.994439	+	0.105316i	$0.966415\pi$
$884$	−145.667	+	25.6849i	−0.164781	+	0.0290554i
$885$		0			0
$886$	−1095.80	+	398.837i	−1.23679	+	0.450154i
$887$	978.326	+	1397.19i	1.10296	+	1.57519i	0.776654	+	0.629928i	$0.216915\pi$
$887$	978.326	+	1397.19i	1.10296	+	1.57519i	0.326307	+	0.945264i	$0.394196\pi$
$888$		0			0
$889$	51.0528	+	60.8424i	0.0574272	+	0.0684391i
$890$	789.292	+	740.833i	0.886845	+	0.832397i
$891$		0			0
$892$	−62.3739	+	62.3739i	−0.0699259	+	0.0699259i
$893$	−61.0571	−	5.34180i	−0.0683730	−	0.00598186i
$894$		0			0
$895$	1382.38	+	198.860i	1.54456	+	0.222190i
$896$	−503.066	+	183.101i	−0.561457	+	0.204354i
$897$		0			0
$898$	346.338	−	494.622i	0.385677	−	0.550804i
$899$	−410.529	+	237.019i	−0.456651	+	0.263647i
$900$		0			0
$901$	−230.991	+	400.088i	−0.256372	+	0.444049i
$902$	−162.859	+	75.9423i	−0.180553	+	0.0841933i
$903$		0			0
$904$	574.943	−	685.190i	0.635998	−	0.757953i
$905$	−427.026	−	335.868i	−0.471852	−	0.371125i
$906$		0			0
$907$	−476.312	+	222.108i	−0.525151	+	0.244882i	−0.667068	−	0.744997i	$-0.732451\pi$
$907$	−476.312	+	222.108i	−0.525151	+	0.244882i	0.141917	+	0.989879i	$0.454673\pi$
$908$	−399.549	+	107.059i	−0.440032	+	0.117906i
$909$		0			0
$910$	603.471	+	141.388i	0.663155	+	0.155371i
$911$	−22.4735	−	127.454i	−0.0246691	−	0.139905i	0.969986	−	0.243162i	$-0.0781847\pi$
$911$	−22.4735	−	127.454i	−0.0246691	−	0.139905i	−0.994655	+	0.103257i	$0.967074\pi$
$912$		0			0
$913$	15.5564	+	7.25406i	0.0170388	+	0.00794530i
$914$	−1186.08	−	209.138i	−1.29768	−	0.228816i
$915$		0			0
$916$	278.119	−	233.370i	0.303624	−	0.254771i
$917$	594.364	−	594.364i	0.648162	−	0.648162i
$918$		0			0
$919$			63.5001i			0.0690970i	0.999403	+	0.0345485i	$0.0109993\pi$
$919$			63.5001i			0.0690970i	−0.999403	+	0.0345485i	$0.989001\pi$
$920$	−114.759	−	128.288i	−0.124738	−	0.139443i
$921$		0			0
$922$	−318.378	−	454.691i	−0.345312	−	0.493157i
$923$	−738.372	−	344.308i	−0.799969	−	0.373032i
$924$		0			0
$925$	−471.686	−	287.603i	−0.509931	−	0.310922i
$926$	−158.686	−	274.853i	−0.171368	−	0.296817i
$927$		0			0
$928$	−1301.57	+	348.753i	−1.40255	+	0.375812i
$929$	−159.618	+	438.546i	−0.171817	+	0.472062i	−0.995475	−	0.0950242i	$-0.969707\pi$
$929$	−159.618	+	438.546i	−0.171817	+	0.472062i	0.823658	+	0.567086i	$0.191929\pi$
$930$		0			0
$931$	−37.4180	−	31.3975i	−0.0401912	−	0.0337244i
$932$	−494.642	+	43.2756i	−0.530732	+	0.0464330i
$933$		0			0
$934$	22.5814	−	62.0419i	0.0241771	−	0.0664260i
$935$	32.4936	+	107.529i	0.0347525	+	0.115005i
$936$		0			0
$937$	−702.528	−	188.242i	−0.749763	−	0.200898i	−0.136350	−	0.990661i	$-0.543537\pi$
$937$	−702.528	−	188.242i	−0.749763	−	0.200898i	−0.613413	+	0.789762i	$0.710204\pi$
$938$	−355.392	+	507.552i	−0.378883	+	0.541101i
$939$		0			0
$940$	−329.460	−	141.112i	−0.350490	−	0.150119i
$941$	117.348	−	665.516i	0.124706	−	0.707243i	−0.856776	−	0.515689i	$-0.827536\pi$
$941$	117.348	−	665.516i	0.124706	−	0.707243i	0.981482	−	0.191554i	$-0.0613528\pi$
$942$		0			0
$943$	−129.819	−	11.3577i	−0.137666	−	0.0120443i
$944$			1664.52i			1.76326i
$945$		0			0
$946$	384.463			0.406410
$947$	−20.6901	+	236.489i	−0.0218481	+	0.249725i	0.977415	+	0.211331i	$0.0677797\pi$
$947$	−20.6901	+	236.489i	−0.0218481	+	0.249725i	−0.999263	+	0.0383939i	$0.987776\pi$
$948$		0			0
$949$	1939.72	+	342.025i	2.04396	+	0.360406i
$950$	74.2615	+	29.0610i	0.0781700	+	0.0305906i
$951$		0			0
$952$	107.230	+	75.0829i	0.112636	+	0.0788686i
$953$	23.5901	−	88.0396i	0.0247535	−	0.0923815i	−0.952444	−	0.304714i	$-0.901439\pi$
$953$	23.5901	−	88.0396i	0.0247535	−	0.0923815i	0.977198	+	0.212332i	$0.0681059\pi$
$954$		0			0
$955$	−299.439	+	558.778i	−0.313549	+	0.585108i
$956$	−310.275	−	112.931i	−0.324556	−	0.118129i
$957$		0			0
$958$	83.1143	+	950.001i	0.0867582	+	0.991650i
$959$	53.1085	−	63.2922i	0.0553790	−	0.0659981i
$960$		0			0
$961$	836.320	+	304.396i	0.870261	+	0.316749i
$962$	−197.942	−	738.728i	−0.205761	−	0.767909i
$963$		0			0
$964$	−139.190	+	80.3615i	−0.144388	+	0.0833626i
$965$	250.351	−	382.780i	0.259431	−	0.396663i
$966$		0			0
$967$	535.715	−	1148.84i	0.553997	−	1.18805i	−0.407492	−	0.913209i	$-0.633597\pi$
$967$	535.715	−	1148.84i	0.553997	−	1.18805i	0.961489	−	0.274842i	$-0.0886255\pi$
$968$	508.858	−	356.306i	0.525680	−	0.368085i
$969$		0			0
$970$	−425.226	−	475.356i	−0.438377	−	0.490058i
$971$	−515.541			−0.530938			−0.265469	−	0.964119i	$-0.585527\pi$
$971$	−515.541			−0.530938			−0.265469	+	0.964119i	$0.585527\pi$
$972$		0			0
$973$	359.420	+	359.420i	0.369394	+	0.369394i
$974$	425.176	+	506.705i	0.436525	+	0.520231i
$975$		0			0
$976$	327.239	−	1855.87i	0.335286	−	1.90150i
$977$	−197.554	+	423.655i	−0.202204	+	0.433628i	−0.981094	−	0.193533i	$-0.938005\pi$
$977$	−197.554	+	423.655i	−0.202204	+	0.433628i	0.778890	+	0.627161i	$0.215783\pi$
$978$		0			0
$979$	317.265	−	55.9425i	0.324071	−	0.0571424i
$980$	−150.577	−	242.723i	−0.153650	−	0.247677i
$981$		0			0
$982$	330.950	+	1235.12i	0.337016	+	1.25776i
$983$	−126.088	−	270.396i	−0.128268	−	0.275072i	0.831677	−	0.555260i	$-0.187381\pi$
$983$	−126.088	−	270.396i	−0.128268	−	0.275072i	−0.959945	+	0.280188i	$0.909603\pi$
$984$		0			0
$985$	−349.770	+	41.7940i	−0.355097	+	0.0424304i
$986$	650.636	+	545.949i	0.659874	+	0.553700i
$987$		0			0
$988$	13.2069	+	28.3223i	0.0133673	+	0.0286663i
$989$	241.460	+	139.407i	0.244146	+	0.140958i
$990$		0			0
$991$	412.360	+	714.229i	0.416105	+	0.720716i	0.995544	−	0.0943004i	$-0.0300614\pi$
$991$	412.360	+	714.229i	0.416105	+	0.720716i	−0.579438	+	0.815016i	$0.696728\pi$
$992$	−165.338	−	115.771i	−0.166671	−	0.116704i
$993$		0			0
$994$	−160.900	−	442.068i	−0.161871	−	0.444737i
$995$	−1226.91	−	176.495i	−1.23307	−	0.177382i
$996$		0			0
$997$	−111.406	+	1273.37i	−0.111741	+	1.27720i	0.708716	+	0.705494i	$0.249275\pi$
$997$	−111.406	+	1273.37i	−0.111741	+	1.27720i	−0.820456	+	0.571709i	$0.806281\pi$
$998$	−476.412	−	476.412i	−0.477367	−	0.477367i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.s.a.118.8		408
3.2	odd	2		135.3.r.a.103.27	yes	408
5.2	odd	4	inner	405.3.s.a.37.8		408
15.2	even	4		135.3.r.a.22.27	✓	408
27.11	odd	18		135.3.r.a.43.27	yes	408
27.16	even	9	inner	405.3.s.a.208.8		408
135.92	even	36		135.3.r.a.97.27	yes	408
135.97	odd	36	inner	405.3.s.a.127.8		408

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.r.a.22.27	✓	408	15.2	even	4
135.3.r.a.43.27	yes	408	27.11	odd	18
135.3.r.a.97.27	yes	408	135.92	even	36
135.3.r.a.103.27	yes	408	3.2	odd	2
405.3.s.a.37.8		408	5.2	odd	4	inner
405.3.s.a.118.8		408	1.1	even	1	trivial
405.3.s.a.127.8		408	135.97	odd	36	inner
405.3.s.a.208.8		408	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.205868 + 2.35308i) q^{2} +(-1.55539 - 0.274257i) q^{4} +(-4.64198 + 1.85797i) q^{5} +(-2.93406 - 2.05445i) q^{7} +(-1.47984 + 5.52284i) q^{8} +(-3.41632 - 11.3055i) q^{10} +(-3.30286 - 1.20214i) q^{11} +(-1.27699 - 14.5961i) q^{13} +(5.43832 - 6.48114i) q^{14} +(-18.6276 - 6.77989i) q^{16} +(1.65433 + 6.17406i) q^{17} +(1.16951 - 0.675215i) q^{19} +(7.72965 - 1.61677i) q^{20} +(3.50870 - 7.52443i) q^{22} +(4.93199 - 3.45342i) q^{23} +(18.0959 - 17.2493i) q^{25} +34.6088 q^{26} +(4.00016 + 4.00016i) q^{28} +(-36.1603 - 43.0941i) q^{29} +(1.46325 - 8.29852i) q^{31} +(10.1229 - 21.7087i) q^{32} +(-14.8687 + 2.62174i) q^{34} +(17.4369 + 4.08532i) q^{35} +(-5.71940 - 21.3451i) q^{37} +(1.34807 + 2.89095i) q^{38} +(-3.39188 - 28.3864i) q^{40} +(-16.5803 - 13.9125i) q^{41} +(19.5707 + 41.9694i) q^{43} +(4.80755 + 2.77564i) q^{44} +(7.11084 + 12.3163i) q^{46} +(-37.1779 - 26.0322i) q^{47} +(-12.3711 - 33.9892i) q^{49} +(36.8637 + 46.1322i) q^{50} +(-2.01687 + 23.0529i) q^{52} +(51.1073 + 51.1073i) q^{53} +(17.5654 - 0.556295i) q^{55} +(15.6883 - 13.1641i) q^{56} +(108.848 - 76.2164i) q^{58} +(-28.7190 - 78.9047i) q^{59} +(16.5080 + 93.6215i) q^{61} +(19.2259 + 5.15156i) q^{62} +(-19.6708 - 11.3569i) q^{64} +(33.0469 + 65.3822i) q^{65} +(-72.9564 + 6.38285i) q^{67} +(-0.879855 - 10.0568i) q^{68} +(-13.2028 + 40.1895i) q^{70} +(27.8020 - 48.1545i) q^{71} +(-34.7929 + 129.849i) q^{73} +(51.4043 - 9.06396i) q^{74} +(-2.00422 + 0.729477i) q^{76} +(7.22105 + 10.3127i) q^{77} +(-24.0782 - 28.6953i) q^{79} +(99.0658 - 3.13742i) q^{80} +(36.1506 - 36.1506i) q^{82} +(-4.86489 - 0.425622i) q^{83} +(-19.1506 - 25.5861i) q^{85} +(-102.787 + 37.4112i) q^{86} +(11.5270 - 16.4622i) q^{88} +(-79.3775 + 45.8286i) q^{89} +(-26.2402 + 45.4494i) q^{91} +(-8.61830 + 4.01878i) q^{92} +(68.9097 - 82.1234i) q^{94} +(-4.17429 + 5.30724i) q^{95} +(48.9432 - 22.8226i) q^{97} +(82.5262 - 22.1128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 408 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 6 q^{8} - 6 q^{10} + 60 q^{11} - 12 q^{13} - 24 q^{16} + 6 q^{17} + 300 q^{20} - 12 q^{22} + 156 q^{23} + 6 q^{25} + 48 q^{26} - 24 q^{28} - 24 q^{31} - 72 q^{32}+ \cdots + 1032 q^{98}+O(q^{100}) \) 408 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 6 * q^8 - 6 * q^10 + 60 * q^11 - 12 * q^13 - 24 * q^16 + 6 * q^17 + 300 * q^20 - 12 * q^22 + 156 * q^23 + 6 * q^25 + 48 * q^26 - 24 * q^28 - 24 * q^31 - 72 * q^32 - 156 * q^35 - 6 * q^37 + 252 * q^38 - 108 * q^40 + 384 * q^41 - 12 * q^43 - 12 * q^46 + 210 * q^47 - 276 * q^50 - 60 * q^52 - 516 * q^53 - 24 * q^55 - 912 * q^56 - 12 * q^58 - 312 * q^61 + 6 * q^62 - 420 * q^65 - 480 * q^67 + 540 * q^68 - 12 * q^70 + 12 * q^71 - 6 * q^73 - 216 * q^76 + 876 * q^77 + 1644 * q^80 - 24 * q^82 + 372 * q^83 - 12 * q^85 - 516 * q^86 + 348 * q^88 - 12 * q^91 - 2082 * q^92 - 198 * q^95 + 600 * q^97 + 1032 * q^98

Introduction

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